Question

Обчислити значення виразу

Answer 1

Ответ:

$\dfrac{1}{3}.$

Объяснение:

$0,125^{-1/3}+0,81^{-1/2}-0,216^{-2/3}=\left(\dfrac{125}{1000}\right)^{-1/3}+\left(\dfrac{81}{100}\right)^{-1/2}-\left(\dfrac{216}{1000}\right)^{-2/3}=$

$=\left(\dfrac{1000}{125}\right)^{1/3}+\left(\dfrac{100}{81}\right)^{1/2}-\left(\dfrac{1000}{216}\right)^{2/3}=\sqrt[3]{8}+\sqrt{\left(\dfrac{10}{9}\right)^2}-\left(\sqrt[3]{\left(\dfrac{10}{6}\right)^3}\right)^2=$

                $=2+\dfrac{10}{9}-\left(\dfrac{5}{3}\right)^2=2+\dfrac{10}{9}-\dfrac{25}{9}=2-\dfrac{15}{9}=2-\dfrac{5}{3}=\dfrac{1}{3}.$